**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 10**

^{11}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 = 10^{5}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 f**

_{0}. 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 10**

^{11}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.**