WAVES MODULE 1READING, QUESTIONS, AND PROBLEMS

INTRODUCTION TO WAVES Read Sections 11-7, 11-8, and 11-9 (first two paragraphs only). Use these sections to answer the following questions:

1. What is a wave?

2. What is the difference between a transverse and a longitudinal wave?

3. What is the difference between the wavelength of a wave and its amplitude?

4. What is the difference between the period of a wave and its frequency?

5. What feature of a wave is related to the energy content of the wave and what is that relationship?

6. What equation relates the period of a wave to its frequency?

7. What is the equation that relates the wavelength of a wave, its frequency, and its speed?

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Name (printed) _______________________________

WAVES MODULE 1For credit, you must provide a clear and complete explanation for each of the following questions.

8. _____ If the amplitude of a wave doubles, its energy increases by a factor ofa. 1.4 b. 1.7 c. 2 d. 4

9. _____ Consider the waves coming from the ocean to the beach. If the wave period increases, the number of waves reaching the beach in one minute willa. increase b. decrease c. remain the same d. can’t be determined

10. _____ The speed of light is 3.0 x 108 m/s. The frequency of light whose wavelength is 5.0 x 10-7 m isa. 6.0 x 1014 Hz b. 6.0 x 1015 Hz c. 1.7 x 1014 Hz d. 1.7 x 1015 Hz

11. _____ A tuning fork has a frequency of 524 Hz. If the speed of the sound is 344 m/sec, what is the approximate wavelength of the sound?a. 0.657 m b. 1.52 m c. 180 m d. 1.80 x 105 m

12. _____ Calculate the wavelength of a sound wave with a speed of 330 m/s and a period of s.a. 0.825 m b. 1.21 m c. 7.58 x 10-6 m d. 1.32 x 105 m

13. _____ A string fixed at both ends as shown in the diagram to the right is set into a standing wave vibration. If the frequency of vibration is 340 Hz, what is the speed of the waves in this string?a. 340 m/s c. 1020 m/s e. 2040 m/sb. 680 m/s d. 1360 m/s

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WAVES MODULE 1LABETTE

INTRODUCTION TO WAVES PURPOSE

• To determine what factors affect wave velocity.• To determine the effects of “open” and “closed” end reflections on waves.• To determine the effect of collisions on colliding waves.

PROCEDURE

I. DETERMINING THE FACTORS THAT AFFECT WAVE VELOCITY1. Stretch the slinky out on the floor to a length of 20 feet. Count the floor tiles, which are each a square foot.

Hold each end of the slinky firmly to the floor.CAUTION: Avoid releasing an end of the stretched spring; the untangling process can be very difficult. Slinkys cost $15 and you WILL be charged.

2. With one end held rigidly in place, give the other end a quick, sharp jerk to the side and then bring it back immediately to its starting position. The pulse generated must have a well-defined beginning and end for your observations to be meaningful. This type of wave pulse is called transverse. Why?

3. Use the stopwatch to measure transverse wave speed. The timing will be rather short, and human reaction time will greatly affect your measurements, so develop a system to avoid human reaction time. Calculate the average time, and then the speed in feet per second.

Trial 1 Trial 2 Trial 3 Trial 4 Average

transversewave time

slinky length: ________ transverse wave speed: ________

4. Repeat step 3 with the Slinky stretched to 30 feet. DO NOT go beyond this length because the Slinky will be damaged! Important: Stretching the slinky to a longer length is changing the medium of the slinky. Again, measure the transverse wave speed in feet per second.

Trial 1 Trial 2 Trial 3 Trial 4 Average

transversewave time

slinky length: ________ transverse wave speed: ________

1. _____ When the spring’s length is reduced, the speed of the pulse a. increases. b. stays the same. c. decreases.

Now generate two pulses of different sizes to see if they travel at the same or different speeds. Generate the two pulses, one immediately after the other. Look to see if the rear pulse catches up with the front pulse, gets further behind, or stays the same distance behind?

2. _____ When the size and shape of the pulse is changed, the speed of the pulsea. changes. b. stays the same.

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WAVES MODULE 1Make a statement about what you have found determines the speed of a wave. Also explain why this is important for the audience of listeners at a concert that has both loud and soft instruments that play both high-pitched and low-pitched sound waves.

II. DETERMINING THE EFFECT OF REFLECTION ON THE WAVE

With the spring stretched back to 20 feet, have your partner hold the far end of the slinky firmly against the floor. Create a sharp, single well-defined pulse. This type of reflection is called a “closed end” reflection. Now have your partner hold the very end of the string. Create a sharp, single well-defined pulse. This type of reflection is called an “open end” reflection.

3. _____ What is the orientation of the reflected pulse when the end is held in place by your hand (closed end)?a. same side of spring b. inverted (other side of spring)

4. _____ What is the orientation of the reflected pulse when the end can move back and forth at the end of the piece of string (open end)?a. same side of spring b. inverted

You should have noticed that the reflections in both cases had the same basic shape, but that the amplitudes were smaller after the reflection. Make a statement about how each of these observations relates to sound wave echoes.

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WAVES MODULE 1III. DETERMINING THE EFFECT OF WAVE PULSE “COLLISIONS”

You and your partner should generate pulses of different sizes from each end of the spring at the same time. Observe what happens when the two pulses meet.

5. _____ When two pulses travel in the same spring from opposite ends they a. bounce off each other b. pass through each other c. destroy each other

6. _____ Again generate two pulses traveling toward each other. Have the two pulses on the same side of the spring as shown to the right. The amplitude of the pulse is the distance from the top of the pulse to the rest position of the spring. When two pulses are produced on the same side of the spring from opposite ends and they meet in the middle, the resulting amplitude isa. zero. c. average of the two.b. less than either pulse. d. greater than either pulse.

7. _____ You probably won’t be able to actually see this, but perhaps you can hypothesize about two pulses of equal amplitude being produced on opposite sides of the spring from opposite ends, as shown to the right. When they meet in the middle, the resulting amplitude isa. zero. b. greater than either pulse.

Use questions 5 and 6 to explain both how you can hear individual conversations at a party attended by multiple people even when they occur together in the same room and also why the loudness of the combined conversations is greater than the loudness of an individual conversation.

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WAVES MODULE 1Questions and Problems

INTRODUCTION TO WAVES 1. The pulse shown below is going into a more rigid medium. Draw the reflected and transmitted pulses in

the empty spaces provided.

2. Let’s say the wave to the below represents the sound wave from a 440 Hz tuning fork. On the line below, draw the shape of the wave coming from a quieter 880 Hz tuning fork.

For credit, you must provide a clear and complete explanation for each of the following questions.

3. _____ A 440 Hz tuning fork is struck and the wave has a particular wavelength. What would happen to the wavelength of the sound wave if a tuning fork with a higher frequency than 440 Hz were used?a. increase b. decrease c. remain the same

4. _____ A 440 Hz tuning fork is struck and the wave has a particular period. What would happen to the period of the sound wave if a tuning fork with a higher frequency than 440 Hz were used?a. increase b. decrease c. remain the same

5. _____ A 440 Hz tuning fork is struck and the wave has a particular speed. What would happen to the speed of the sound wave if a tuning fork with a higher frequency than 440 Hz were used?a. increase b. decrease c. remain the same

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After

Before More rigid

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WAVES MODULE 1QUESTIONS AND PROBLEMS INTRODUCTION TO SOUND

1. The temperature is -20°C. What is the speed of sound?

2. An ultrasonic sound wave has a frequency of 45,000 Hz and a speed in air of 342 m/s. What is the air temperature?

3. What is the ratio of the speed of sound in air at 0° C to the speed at 100° C?

4. You’re in the alps and want to try your yodeling skills. You give a holler toward a cliff 515 m away and wait for the echo to return. How long do you have to wait?

5. The Ocular Hypertension Treatment Study (OHTS) a few years ago found a link between corneal thickness and the probability of getting glaucoma. Many optometrists now use a ultrasound device to calculate the thickness of the cornea. The device produces sound waves that move at 1500 m/s from the front surface of the cornea to the back surface and then reflect back. The device uses the amount of time for the echo of the sound waves to return to calculate the thickness of the cornea. If the time for the echo to return in a particular patient is 8.0 x 10-7 s, what is the thickness of the cornea?

6. How many times louder is 79 dB sound than a 73 dB sound?

7. What is the number of decibels that is 16 times louder than 84 dB?

8. What is the decibel level of a sound that is 20 times quieter than 95 dB?

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WAVES MODULE 1

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WAVES MODULE 19. How many times louder is 90 dB sound than a 64 dB sound?

10. What is the decibel level of a sound that is 16,000 times quieter than 86 dB?

11. What is the decibel level of the sound that is 2,000 times quieter than 12 dB

Problems 12 – 16 are for Honors Physics only12. If you double your distance from a sound source, how many decibels will the sound intensity level drop to?

13. Three students clapping their hands produce a sound intensity level of 88 dB. They have just finished listening to a stunning physics lecture. Their 29 colleagues feel the same as them and begin clapping with the same intensity. To what level does the decibel level rise?

14. It’s a good idea to make sure that you keep the chronic sound you’re exposed to less than 80 dB. If you were working 1.0 m from a machine that created a sound intensity level of 92 dB, how far would you need to move from the machine in order to only hear 80 dB? (Hint: remember to compare sound intensities and not sound intensity levels.)

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WAVES MODULE 115. 250 freshmen at Tamalpais High School give a class cheer which registers at 92 dB. 200 seniors then give a

cheer which registers at 98 dB. a. What is the ratio of the average freshman’s sound intensity (not sound intensity level) to that of the average senior’s sound intensity?

b. If the original decibel readings were taken five meters away from each class, how far from the senior class would you have to stand to get the same decibel level as the freshman class?

16. At the Tamalpais High School Farewell Rally of 2009, the popular class cheer competition occurred about midway through the rally. The following are the results of that competition:

Freshmen – 106.9 dB Sophomores – 108.4 dBJuniors – 118.8 dB Seniors – 121.2 dB

a. By what factor did the Senior Class sound intensity exceed that of each of the Freshman Class sound intensity?

b. The measurements were taken from 9.0 m from the center of each class. What was the total power (in Watts) of the Senior Class?

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WAVES MODULE 1LABETTE

SPEED OF SOUND Note: Please do not strike the tuning forks against any hard surface. This alters their frequency.

Vibrating a medium at what is known as the resonant frequency will cause a large increase in amplitude. This can be heard in musical instruments and seen in buildings and bridges. In this lab, the speed of sound can be determined if we know the resonance frequency for air vibrating in an air column as well as the air column’s length.

PURPOSEDetermine the speed of sound by measuring the length of an air column vibrating at its fundamental frequency (also called the first harmonic mode of oscillation).

PROCEDURE, DATA, & ANALYSIS (Show all work)1. Check the thermostat reading for room temperature in degrees

Fahrenheit. Then convert into degrees Celsius using:

2. Determine actual (known) speed of sound:

= _______ m/s

3. Place the plastic tube into the 100-milliliter graduated cylinder and fill the cylinder with water to the 80-ml mark.

4. Select a tuning fork and record its frequency.

Frequency, f = _______ Hz

5. Strike the tuning fork with the rubber mallet and hold it about 1 cm above the open end of the tube. Move both the fork and the tube up and down to find the air column length that gives the loudest sound. Important: this loud sound will be at the same frequency as the tuning fork. Listen to the tuning fork and then the resonating air column to be sure.

6. Measure the actual length of the air column in meters. Remember that this is the distance from the surface of the water to the top of the plastic tube.

Actual Length, L = ________ m

7. It turns out that the air resonates slightly above the tube. This point is influenced by the diameter of the air column. We must correct for this by adding to the Actual Length (L). Measure the inside diameter of the tube (in meters), and multiply by 0.4.

Diameter of tube = ________ m Diameter x 0.4 = _______ m

Effective length of air column, Leff = Actual Length (L) + (Diameter x 0.4) = _______m

8. The wavelength of the sound wave is four times the effective length of the air column (Leff) (you will see why next week!). With the equation , calculate the speed of sound

Wavelength, = 4Leff = _______ m

Speed of sound in air, v = f = ________ m/s

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WAVES MODULE 1Tuning fork #2 (show work in space provided)

Frequency, f = _______ Hz

Length, L = ________ m

Effective length of air column, Leff = Length (L) + (Diameter x 0.4) = _______ m

Wavelength, = 4Leff = _______ m

Speed of sound in air, v = f = ________ m/s

Tuning fork #3 (show work in space provided)

Frequency, f = _______ Hz

Length, L = ________ m

Effective length of air column, Leff = Length (L) + (Diameter x 0.4) = _______ m

Wavelength, = 4Leff = _______ m

Speed of sound in air, v = f = ________ m/s

QUESTIONS & CALCULATIONS1. Calculate the average experimental speed of sound measured by the three tuning forks.

2. Calculate the percent error between the average experimental speed of sound and the known speed of sound determined earlier, based on air temperature.

_______%

3. Look at the data for the lowest and highest frequency tuning forks. Which one resonated with the longest wavelength? The shortest wavelength? Make a brief statement about the physical size of any wind instrument and the frequency of sounds it can produce.

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WAVES MODULE 1Questions and Problems

THE DOPPLER EFFECT 1. A woman who doesn’t appreciate the improper advances of a rude thug blasts him with some pepper spray.

She then screams that her next move will be to give him a little “lead poisoning” from her licensed firearm, which she lovingly refers to as “my li’l equalizer.” The frequency of her scream is a piercing 1,000 Hz on an evening when the air temperature is a brisk 10°C. If the thug starts sprinting away from the woman at a speed of 7 m/s, what frequency will he hear?

2. The thug didn’t run fast enough and ... he’s down for the count. You happen to be in the area driving at a speed of 25 m/s when the ambulance, called to remove his riddled remains, approaches from behind at 45 m/s and with a siren frequency of 1,400 Hz. El Niño has lowered the temperature to a bitter -5°C. You hear a different frequency from the siren before it passes you compared to after it passes you. What is the difference in the frequencies you hear?

3. You’re still traveling down the highway at 25 m/s when the ambulance returns, this time approaching you from the front at the same 45 m/s. The temperature hasn't changed either. What is the difference in frequency you hear this time as the ambulance approaches and then passes you?

4. A train approaches a station at a speed of 34 m/s and sounds a 2000-Hz whistle. What is the change in frequency heard as the train passes by?

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WAVES MODULE 15. An observer approaches a stationary 1000 Hz sound source at twice the speed of sound. What frequency does

the observer hear?

6. If an X-15 jet, producing a frequency of 900 Hz, were moving away from you at 2.5 times the speed of sound, what frequency would you hear?

7. The wave below represents a sound wave from a siren heard by a stationary observer far away from the siren. On the blank line below, draw what the sound wave would be like to the observer as he moved closer and closer toward the siren at a high constant speed. (I’m looking for three things to be illustrated in your drawing).

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