Question

A hammer taps on the end of a 4.00 m long metal bar at room temperature. A microphone at the the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through air. The pulse traveling through the metal arrives 9ms earlier because sounds travels faster through solids than air. What is the speed of the sound in the metal? Speed of sound through air is 343 m/s at room temperature. Give your answer in units of m/s but do not include units,

Answer 1

The speed of sound in the metal is 444.44 m/s.

Step-by-step explanation:

To determine the speed of sound in the metal, we can use the information given and the speed of sound in air. The pulse traveling through the metal arrives 9ms earlier than the pulse traveling through air. From this, we can calculate the time difference it takes for the pulses to travel through the length of the metal bar. The speed of sound in air is given as 343 m/s. We can use the formula: speed = distance/time. Rearranging the formula, we have: time = distance/speed. As the distance is given as 4.00 m and the time difference is given as 9 ms (0.009 s), we can calculate the speed of sound in the metal by dividing the distance by the time difference: speed = 4.00 m / 0.009 s = 444.44 m/s.

Answer 2

`v_m=193.5939\ m.s^(-1)`

Step-by-step explanation:

• distance travelled by the sound,
  `l= 4\ m`

• speed of sound in air,
  `v_a=343\ m.s^(-1)`

• difference of time time between the two pulses of sound,
  `\Delta t=0.009\ s`

Now, we find the time taken by the sound in air to travel the given distance:

`t_a=(l)/(v_a)`

`t_a=(4)/(343)`

`t_a=0.011662\ s`

∴Time taken by the sound sound waves in the metal bar to travel the given distance:

`t_m=t_a+\Delta t`

`t_m=0.011662+0.009`

`t_m=0.020662\ s`

The speed of sound in the metallic bar:

`v_m=(l)/(t_m)`

`v_m=(4)/(0.020662)`

`v_m=193.5939\ m.s^(-1)`