A bat emits ultrasonic sound of frequency \(1000Khz\) in air. If this sound meets a water surface, what is the wavelength of (a) the reflected sound. (b) the transmitted sound? Given: Speed of sound in air \(=340\frac{m}{s}\) and in water \(=1486\frac{m}{s}\).
Ans:(a) \(\lambda_{air}=\left(3.4\times10^{-4}\right)m\) and (b) \(\lambda_{water}=\left(1.49\times10^{-3}\right)m\).
If a sound is heard \(4.23Sec\) after a stone stone is dropped into a well \(78.4m\) deep. Find: the speed of sound in air.
Ans: \(V_{air}=340.57\frac{m}{s}\).
Audible frequencies have a range \(20Hz\) to \(20KHz\). Express the range in terms of (a) Period T. (b) Wavelength \(\lambda\) in air. and (c) angular frequency. Given: Velocity of sound in air \(330\frac{m}{s}\).
The speed of transverse wave in a stretched string is \(348\frac{m}{s}\), when the tension in string is \(3.6kg-wt\). Calculate: the speed of transverse wave in the same string, if tension in the string is changed to \(4.9Kg-wt\).
Ans: \(V_{2}=406\frac{m}{s}\).
A string is under tension of \(100N\). the mass and the length of the string is \(1Kg\) and \(10m\) respectively. How much time the waves take to go from one end to the other end.
Ans: \(t=0.32Sec\).
A copper wire is held at the two ends by rigid supports. At \(30^{o}C\), the wire is just taut with negligible tension. Find: the speed of transverse waves in the wire at \(10^{o}C\). Given: \(\alpha=\left(1.7\times10^{-5}\right)^{o}C^{-1}\).
Ans: \(V=72\frac{m}{s}\).
Calculate: the speed of the mechanical waves in a rail road track made of steel. Young’s modulus for steel is \(\left(2\times10^{11}\right)\frac{N}{m^{2}}\), its density is \(\left(7.8\times10^{3}\right)\frac{kg}{m^{3}}\). If the frequency of the source is \(240Hz\), What is the wavelength of the wave in steel?
Ans: \(\lambda=21.1m\).
The value of bulk modulus and the modulus of rigidity for aluminum are \(\left(7.5\times10^{10}\right)\frac{N}{m^{-2}}\) and \(\left(2.1\times10^{10}\right)\frac{N}{m^{-2}}\). Calculate: the velocity of the longitudinal waves in the medium if the density of aluminum is \(\left(2.7\times10^{3}\right)\frac{kg}{m^{3}}\).
The longitudinal waves starting from a ship returns from the bottom of the sea to the ship after \(2.64s\). If, the bulk modulus of water is \(220\frac{kg}{mm^{2}}\) and density \(\left(1.1\times10^{3}\right)\frac{kg}{m^{3}}\). calculate: the depth of the sea. Take: \(g=9.8\frac{N}{kg}\).
Ans: \(Depth_{sea}=1848m\).
Calculate: the speed of sound in air at standard temperature and pressure by using (i) Newton’s formula and (ii) Laplace formula. The mass of one mole of air \(\left(29\times10^{-3}\right)kg\). Take: \(\gamma_{air}=1.4\).
Ans:(i) \(V_{Newton}=280\frac{m}{s}\) and (ii) \(V_{Laplace}=331.5\frac{m}{s}\).
At normal temperature and pressure, \(4g\) of helium occupies a volume of \(22.4Litres\). Determine: the speed of sound in helium. Take: \(\gamma_{He}=1.67\) and 1 atmospheric pressure \(=10^{5}\frac{N}{m^{-2}}\).
