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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 :

Answer:

The wavelength of the wave is 20 m.

Explanation:

Given that,

Amplitude = 10 cm

Radial frequency [tex]\omega = 20\pi\ rad/s[/tex]

Bulk modulus = 40 MPa

Density = 1000 kg/m³

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

Using formula of velocity

[tex]v=\sqrt{\dfrac{k}{\rho}}[/tex]

Put the value into the formula

[tex]v=\sqrt{\dfrac{40\times10^{6}}{10^3}}[/tex]

[tex]v=200\ m/s[/tex]

We need to calculate the wavelength

Using formula of wavelength

[tex]\lambda =\dfrac{v}{f}[/tex]

[tex]\lambda=\dfrac{v\times2\pi}{\omega}[/tex]

Put the value into the formula

[tex]\lambda=\dfrac{200\times2\pi}{20\pi}[/tex]

[tex]\lambda=20\ m[/tex]

Hence, The wavelength of the wave is 20 m.

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