Question

Two identical loudspeakers 2.00 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 5.50 m in front of one of the speakers perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound. What is the lowest possible frequency of sound for which this is possible? Express your answer with the appropriate units.

Answer 1

The lowest possible frequency of sound is 971.4 Hz.

Step-by-step explanation:

Given that,

Distance between loudspeakers = 2.00 m

Height = 5.50 m

Sound speed = 340 m/s

We need to calculate the distance

Using Pythagorean theorem

`AC^2=AB^2+BC^2`

`AC^2=2.00^2+5.50^2`

`AC=√((2.00^2+5.50^2))`

`AC=5.85\ m`

We need to calculate the path difference

Using formula of path difference

`\Delta x=AC-BC`

Put the value into the formula

`\Delta x=5.85-5.50`

`\Delta x=0.35\ m`

We need to calculate the lowest possible frequency of sound

Using formula of frequency

`f=(nv)/(\Delta x)`

Put the value into the formula

`f=(1*340)/(0.35)`

`f=971.4\ Hz`

Hence, The lowest possible frequency of sound is 971.4 Hz.