Unit 11

163 Your Turn Solutions


1. Lotta Kareoake sings a C wave with a 250 Hz pitch. If the temperature is 20o Celsius, determine:

a. The speed of the wave.

b. The length of one of the 250 Hz waves.

2. Yoda Lehihue yells toward a cliff 680 meters away. A reflected wave is detected 4.0 seconds after Yoda yells (it travels there and back).

a. Determine the speed of sound in air.

b. Determine the wavelength of the sound wave if its frequency is 500 Hz.

c. Determine the period of the wave.

3. The speed of sound in air is 340 m/s. A sound wave has a 750 Hz pitch.

a. Determine the 750 Hz wavelength as it travels through air.

b. Determine the period of the 750 Hz wave.

4. The sound wave created in air with a pitch of 750 Hz travels through air and into water. If it enters water which increases the speed of sound to 1480 m/s:

a. Determine the frequency of the transmitted 750 Hz wave when it is in the water.

750 Hz

 

b. Determine the wavelength of the transmitted 750 Hz wave when it is in the water.

5. 1400 Hz wave created inside an aluminum bar has a wavelength of 3.57 m inside the aluminum.

a. Determine the velocity of the 1400 Hz wave while in the aluminum.

b. If the 1400 Hz wave enters the air and travels at 340 m/s, determine its wavelength in the air.

6. A sonar signal generated with a frequency of 1 x 106 Hz has a wavelength of 1.5 mm in water.

a. Determine the speed of the signal in water.

b. Determine the period of the signal in water.

c. Determine the period of the same signal if it is transmitted from the water into the air.

T=10-6s. If frequency is constant, period is constant.

7. The speed of sound in water is 1489 m/s. A sonar signal is sent from a ship at a point just below the water surface and 2.14 seconds later the reflected signal is detected. How deep is the ocean beneath the ship?

A student holds a spring at both ends and tries to shake the spring at just the right frequency to generate the first and second resonances on the slinky.

 

8. Explain whether the ends are open or closed.

The ends are closed because they are both at his hands.

 

9. Box the portion of the standing wave below that would resonate fundamentally.

Your box should enclose the entire wave from the first node to the second node.

10. Expand the wave in the boxed area to fit on the slinky below.

Your picture should just have the one segment you boxed with a node at each end of the slinky.

11. Compare the length of the slinky to the wavelength of the resonating wave.

12. Explain whether the ends are open or closed.

Both ends are closed because both ends are antinodes.

13. Box the portion of the standing wave below that would resonate at the next harmonic.

You should have boxed the entire wave until the second crest.

14. Expand the wave in the boxed area to fit on the slinky below.

Just take your boxed part and widen it until it is at the end of the line.

15. Compare the length of the slinky to the wavelength of the resonating wave.

16. Explain whether the ends are open or closed.

One of the ends is closed (the node). The other end is open (the antinode).

17. Box the portion of the standing wave below that would resonate at the third resonant frequency.

Box all the way to the third crest.

18. Expand the wave in the boxed area to fit on the slinky below.

Same thing as before.

19. Compare the length of the slinky to the wavelength of the resonating wave.

20. A flute acts like an open tube with an air column inside that resonates with a fundamental frequency of 370 hz. Determine:

a. The second harmonic of the flute's air column.

740 Hz

b. The third harmonic of the flute's air column.

1110 Hz

c. The sixth harmonic of the flute's air column.

1480 Hz

21. If a bugle (an open pipe) were straightened out, it would be 2.65 meters long. If the speed of sound is 343 m/s, find the lowest frequency that will resonate in a bugle.

22. A soprano saxophone (another open pipe) is approximately 65 cm long when all keys are closed. If the temperature of the air is 23o C, determine:

a. the lowest frequency that can be played in the sax.

b. the second, third and fourth harmonics played by the soprano sax.

(264.5 Hz)(2)=529 Hz

(264.5 Hz)(3)=793 Hz

(264.5 Hz)(3)=1058 Hz

23. A pipe organ uses open and closed tubes in order to play the large variety of frequencies (notes) demanded by its players. The loudest frequency that is heard from each tube is its fundamental frequency.

a. Determine the length of pipe needed for each of the given frequencies

below for open pipes on a day where the speed of sound is 340 m/s.

LOW C (f1 = 256 Hz)

D (f1 = 288 Hz)

B (f1 = 480 Hz)

MIDDLE C (f1 = 512 Hz)

b. Determine the length of pipe needed for each of the given frequencies

below for closed pipes on a day where the speed of sound is 340 m/s.

 

LOW C (f1 = 256 Hz)

D (f1 = 288 Hz)

B (f1 = 480 Hz)

MIDDLE C (f1 = 512 Hz)

24. Two horn players are attempting to play a 70 Hz tone but a beat frequency of 2 Hz is heard. One of the horns is playing 70 hz. What is are possible frequencies of the other horn?

The other horn could be playing at either 68 Hz or 72 Hz.

25. A bolt of lightning strikes across town which you notice. 10 seconds later you hear the thunder. Assuming the light got to you almost instantly (light travels at 300,000,000 m/s...instantly is a good approximation) determine how far away the lightning strike was in:

a. meters.

b. miles.


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Last Updated: October 8, 1997