## Saturday, 6 September 2014

### SOUND PROBLEMS

Sound

1. A small explosion is set off on a railway line and an observer 1 km away with one ear to the rail hears two reports. Using only the following data find the time interval between them.
(Young modulus for steel = 2 x 1011 Pa, density of steel = 7800 kgm-3; density of air = 1.3 kgm-3; ratio of the principal specific heat capacities for air = 1.4; atmospheric pres­sure = 105 Pa.)

2. It is possible to make a toy telephone from two tins with a taut stretched string between them. How does this work? Why is the transmitted sound louder than the sound travelling through air for the same distance?

3. When sound waves travel from air into water which of the following change: frequency, wavelength, vel­ocity?
4. A horizontal metal wire is fixed in a state of tension between two vertical supports. When plucked it gives a fundamental frequency f0. What change, if any, will be observed in this fundamental frequency if the wire is now immersed in water and plucked again? Explain your answer.

5. A steel wire is hung from one end and kept in a state of tension by a mass of iron fixed to the lower end. When the wire is plucked in air it emits a note frequency 256 Hz. What will be the new frequency if the wire is suspended vertically in water?
(Density of iron = 7800 kgm-3; density of water = 1000 kg m-3.)

6. Calculate the following:
(a)  the frequency of BBC Radio 4, wavelength 1500 m;
(b)  the wavelength of the sound of frequency 256 Hz (middle C);
(c)  the fundamental frequency of a string of length 1 m and mass per unit length 2g when the tension in the string is 10 N;
(d)  the velocity of the travelling waves in (c).

7. Find the ratio of the frequencies of transverse and longitudinal vibrations in a steel sonometer wire of diameter 1.5 mm and tension 100 N.
(Young's mod­ulus for steel = 2 x 1011 Pa)

8. In a resonance tube experiment using a tuning fork with a frequency of 512 Hz the first two resonant positions occur with tube lengths of 13.6 cm and 43.5 cm respectively. Calculate
(a)  the velocity of sound, and
(b)  the end correction for the tube.

9. Two organ pipes 80 cm and 81 cm long are found to give a beat frequency of 2.6 Hz when each is sounding its fundamental note. Neglecting end correc­tions calculate from these results:
(a)  the velocity of sound in air, and
(b)  the frequencies of the two notes.