Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. (a) In a liquid with density 1300 kg/m3, longitudinal waves with frequency 400 Hz are found to have wavelength 8.00 m. Calculate the bulk modulus of the liquid. (b) A metal bar with a length of 1.50 m has density 6400 kg/m3. Longitudinal sound waves take 3.90 X 10-4 s to travel from one end of the bar to the other. What is Young’s modulus for this metal?
Assume the speed of sound in air to be v = 344 m/s. (a).Bulk modulus of liquid is calculated by Given data: Liquid density = 1300 kg/m 3 Wavelength = 8 m Frequency of wave f = 400 Hz Consider v = f = 400(8) = 3200 m/s. v = B/ v = B/ Where B is the bulk modulus constant 2 B = v 3 2 B = (1300 kg/m )(400) B = 1.3312 × 10 pa (b).For metal bar: Given data: d = length of the bar = 1.5 m Metal density = 6400 kg/m 3 t = time of wave travel = 3.9 × 10 4s Consider v = d/t = 1.5 m/(3.9 × 10 s) = 3846.15 m/s. v = / v = Y / Where Y is the young’s modulus constant Y = v 2 Y = (6400 kg/m )(400) 2 B = 9.467 × 10 pa0
