Question

A 4 m long metal bar tapped by a hammer on one end. A microphone recording the sound at the other end picks up two sound pulses; one which traveled through the metal bar and other which was traveling through room temperature air. These two pulses are separated by 11 msec. What is the speed of sound in the metal

Answer 1

To find the speed of sound in the metal, first calculate the distance sound travels in room temperature air during the 11 msec time difference. Next, use the known distance of the metal bar and this time difference to calculate the speed of sound in the metal, which is approximately 363.64 m/s.

Step-by-step explanation:

To calculate the speed of sound in the metal, we use the information that the sound pulse travels through the metal bar faster than through the room temperature air, resulting in a time difference of 11 milliseconds (msec). Since the speed of sound in air is given as 346 m/s, we can calculate the distance that sound travels in air in 11 msec. We then use this distance and the time difference to find the speed of sound in the metal by utilizing the formula: speed = distance / time.

First, convert the time difference to seconds: 11 msec = 0.011 seconds.

Now, calculate the distance sound traveled in air using the speed of sound in air:

distance_air = speed_air * time_difference = 346 m/s * 0.011 s = 3.806 m.

This means the sound traveled 3.806 m through the air while it traveled the entire 4 m length of the metal bar. We now set up the equation for the speed of sound in the metal:

speed_metal = distance_metal / time_difference = 4 m / 0.011 s.

Calculating this gives us the speed of sound in the metal:

speed_metal = 4 m / 0.011 s = approximately 363.64 m/s.

Answer 2

Step-by-step explanation:

Speed of sound in air at room temperature = 346 m /s

Let speed of sound in metal given = v m /s

Time take by sound wave travelling through air = 4 / 346 = .01156 s

Time taken by sound wave travelling through metal = 4 / v s

Given ,

.01156 - 4 / v = 11 x 10⁻³ s = .011 s ( time taken by sound travelling in air is more )

4 /v = .01156 - .011 = .00056

v = 4 / .00056 = 7142.85 m /s