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hodyreva [135]
3 years ago
9

A wave on a string is described by D(x,t)= (2.00cm)sin[(12.57rad/m)x−(638rad/s)t], where x is in m and t is in s. The linear den

sity of the string is 5.00g/m.
What is the string tension?

What is the maximum displacement of a point on the string?

What is the maximum speed of a point on the string?
Physics
1 answer:
mamaluj [8]3 years ago
5 0

Answer : The string tension is T = 12.882 N

The maximum displacement is 0.02 m

The maximum speed is v = 12.76\ m/s

Explanation :

Given that,

D(x,t) = (2.00 cm) sin [(12.57rad/m)x - (638rad/s)t]

Where, x is in m and t is in sec.

Linear density of the string = 5.00 g/m

We know that,

Velocity of the wave

v = \dfrac{\omega}{k}

v = \dfrac{638}{12.57}\ m/s

v = 50.76\ m/s

Now, the string tension

v = \sqrt\dfrac{T}{m}

T = 0.005\times (50.76)^{2}\ N

T = 12.882 N

The maximum displacement is 0.02 m

The maximum speed  

v = a \omega

v = 0.02\times638\ m/s

v = 12.76\ m/s

Hence, this is the required solution.





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now,

   \dfrac{y}{D} = 1.22\dfrac{\lambda}{d}

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40 m=4\lambda

Clearing \lambda:

\lambda=\frac{40 m}{4}

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If 10 waves ---- 16 s

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