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boyakko [2]
3 years ago
15

A man strikes one end of a thin rod with a hammer. The speed of sound in the rod is 15 times the speed of sound in air. A woman,

at the other end with her ear close to the rod, hears the sound of the blow twice with a 0.12 s interval between; one sound comes through the rod and the other comes through the air alongside the rod. If the speed of sound in air is 343 m/s, what is the length of the rod?
Physics
1 answer:
lina2011 [118]3 years ago
4 0

Answer:

44.1 m

Explanation:

<u>Given:</u>

  • V_a = speed of sound in air = 343 m/s
  • V_r = speed of sound in the rod = 15V_a
  • \Delta t = times interval between the hearing the sound twice = 0.12 s

<u>Assumptions:</u>

  • l = length of the rod
  • t = time taken by the sound to travel through the rod
  • T = time taken by the sound to travel to through air to the same point = t+\Delta t = t+0.12\ s

We know that the distance traveled by the sound in a particular medium is equal to the product of the speed of sound in that medium and the time taken.

For traveling sound through the rod, we have

l=V_r t\\\Rightarrow t = \dfrac{l}{V_r}..........eqn(1)

For traveling sound through the air to the women ear for traveling the same distance, we have

l=V_aT\\\Rightarrow l=V_a(t+0.12)\\\Rightarrow l=V_a(\dfrac{l}{V_r}+0.12)\,\,\,\,\,\,(\textrm{From eqn (1)})\\\Rightarrow l=V_a(\dfrac{l}{15V_a}+0.12)\\\Rightarrow l=\dfrac{l}{15}+0.12V_a\\\Rightarrow l-\dfrac{l}{15}=0.12V_a\\\Rightarrow \dfrac{14l}{15}=0.12V_a\\\Rightarrow l = \dfrac{15}{14}\times 0.12V_a\\\Rightarrow l = \dfrac{15}{14}\times 0.12\times 343\\\Rightarrow l = \dfrac{15}{14}\times 0.12\times 343\\\Rightarrow l = 44.1\ m

Hence, the length of the rod is 44.1 m.

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