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masya89 [10]
3 years ago
12

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.
Physics
1 answer:
nydimaria [60]3 years ago
5 0

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.

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