Question

Find the wavelength in meters for a transverse mechanical wave with an amplitude of 10 cm and a radian frequency of 20π rad/s if the medium through which it travels has a bulk modulus of 40 MPa and a density of 1000 kg/m^3.

Answer 1

Answer:

The wavelength of the wave is 20 m.

Explanation:

Given that,

Amplitude = 10 cm

Radial frequency $\omega = 20\pi\ rad/s$

Bulk modulus = 40 MPa

Density = 1000 kg/m³

We need to calculate the velocity of the wave in the medium

Using formula of velocity

$v=\sqrt{\dfrac{k}{\rho}}$

Put the value into the formula

$v=\sqrt{\dfrac{40\times10^{6}}{10^3}}$

$v=200\ m/s$

We need to calculate the wavelength

Using formula of wavelength

$\lambda =\dfrac{v}{f}$

$\lambda=\dfrac{v\times2\pi}{\omega}$

Put the value into the formula

$\lambda=\dfrac{200\times2\pi}{20\pi}$

$\lambda=20\ m$

Hence, The wavelength of the wave is 20 m.