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2 years ago

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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.

1 answer:

nydimaria [60]2 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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Answer:

a) $h_m=74625\ m$

b) $t=265.55\ s$

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$v_f^2=u^2+2a.h_f$

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<u>During the phase of ascend in height of rocket after the fuel is over:</u>

<u>Time taken to reach the top height after the fuel is over:</u>

$v=v_f+g.t'$

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$v^2=v_f^2+2g.h'$

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$0^2=1050^2-2\times 9.8\times h'$ (-ve sign denotes that the direction of motion is opposite to that of acceleration)

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b)

time taken by the rocket to fall back to the earth:

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$v=$ initial velocity of the rocket during the course of free fall from the top height.

$74625=0+4.9\times t_m^2$

$t_m=123.41\ s$

Now the total time for which the rocket is in the air:

$t=t_f+t'+t_m$

$t=35+107.1429+123.41$

$t=265.55\ s$

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