Physics 112 Problems: Sound 1

Wavelength

1. When the Tair = 25⁰ C, a 412 Hz tuning fork will release a sound wave of what length?

2. A tuning fork of what frequency produces a 3 m long sound wave when the Tair is 20⁰C?

3. Find the wavelength of the sound from a 400 Hz tuning fork if the Tair is 25⁰C.

Temperature-Distance

4. How long will it take a sound to travel 1 km when the Tair is 10⁰?

5. At - 10⁰C, how far will a sound travel in 2.5 s?

6. Twenty seconds after a lightning flash is seen, a rumble of thunder is heard. How far away is the lightning flash if the Tair is 28⁰?

7. A sound travels the same distance through two materials. It moves through the slower one at 340 m/s and through the other at 5 000 m/s. If it takes 5 s longer for the sound to move along the slower path, what is the distance it travels through the two materials?

8. A train robber listens on a steel rail for the sound of an approaching train. The rumble arrives 5.7 s sooner through the rail than through the air. If the sound moves at 4 970 m/s through the steel and the Tair = 15⁰ C, how far away is the train? (Hint: v in air)

9. A girl some distance from you hammers on a steel rail and you hear the sound through the track 15 s sooner than through the air. If the sound moves at 355 m/s in air and 5 009 m/s in steel, how far away is the girl?

Echoes

10. A coastal steamer sounds its whistle and the echo returns in 3 s. If the sound moves at 340 m/s, how far away is the shore?

11. When the Tair = - 5⁰ C, a ship's fog horn echo returns in 7 s. How far away is the reflecting surface?

12. A coyote sitting in a valley howls and the echo from one valley wall is heard in 3 s. The echo from the other wall arrives 4 s later. If the Tair = - 15⁰ , find the valley width.

13. A girl standing in a valley fires her rifle. The echo from one wall is heard in 3 s and the echo from the other wall is heard 6 s later. If the Tair is 5⁰, find the width of the valley.

14. A girl in a gym wants to hear an echo and claps her hands. If the echo returns in less than 0.1 s, her ear can not distinguish it from the original clap. If the sound travels at 350 m/s, the girl would have to stand at least how far from the wall to ensure that the echo does return at least 0.1 s after the original sound is made?

Laws of Strings

15. A 100 cm long string produces a 200 cps fundamental tone. If the string is held 25 cm from one end, what are the frequencies produced by each segment. (Hints: your finger divides the string into how may segments? The length of each?)

16. a) A 100 cm. long wire tensioned to 19.6 N produces a frequency of 300 Hz. What length will sound at 600 Hz if the tension is not altered?
b) Now, find the frequency using the answer from a) but changing the tension to 78.4 N.

17. A 200 cm long string tensioned to 30 N sounds at 400 Hz. Find string's frequency when its length is reduced to 125 cm. and its tension to 15.0 N.

18. A 0.5 cm diameter, 200 cm long string produces a frequency of 400 Hz. when it is tensioned to 18 N The string would sound at what frequency if its diameter were 0.2 cm and its length were 100 cm?

19. A 100 cm long string of density 6.5 gm/cm³ sounds at 256 Hz. At what frequency would it sound if its tension and diameter are kept constant, but the length is shortened by 50 cm and the density increased to 13 g/cm³?

20. A 100 cm long string tensioned to 20 N sounds at 225 Hz. Find the frequency produced if the length is reduced to 25 cm and the tension reduced to 5 N.

21. A 200 cm long, 0.2 cm diameter string tensioned to 18 N sounds at 400. Hz. At what frequency would it sound if the length were 100 cm and the tension were 72 N?

Resonance in Tubes

22. At 20⁰, an open, 24 cm long, 3 cm diameter tube resonates with a tuning fork of what frequency?

23. At 20⁰; a closed, 2 cm diameter tube of what length will resonate with a 256 Hz tuning fork?

24. If the speed of sound is 340 m/s, a closed, 2 cm diameter pipe of what length is required to produce a 440 Hz fundamental tone?

25. A 50 cm long, 4 cm diameter organ pipe open at both ends produces what fundamental frequency at 0⁰?

26. If the speed of sound is 340 m/sec., a closed, 2 cm diameter pipe of what length will produce a 440 cps fundamental tone?

27. A pipe open at both ends resonates to a fundamental frequency of 300 Hz. What is the next higher frequency to which it will resonate?

28. At 27⁰, an open, 2.5 cm diameter tube of what length will resonate with a 338 c/s tuning fork?

29. At 15⁰, a closed, 13.6 cm long, 1.5 cm diameter tube would resonate with a tuning fork of what frequency?

30. An open and a closed tube, both 3.0 cm diameter, both resonate with a 512 Hz. tuning fork. Find the lengths of the two tubes if the Tair is 20 ⁰.

Beats

31. An 40 cm long, 2 cm diameter open tube is sounded with a 20 cm, 2.5 cm diameter closed tube. If the Tair is 25⁰, what will be the beat frequency? (Hint: find and subtract the two f's.)

32. A 256 Hz and a 300 Hz tuning fork sounded simultaneously create what beat frequency?

33. When a 256 Hz. tuning fork is sounded with a tuning fork of undetermined frequency, 12 beats/sec. are observed. What could be the frequencies of the second tuning fork?