Question

You are standing 2.5 m directly in front of one of the two loudspeakers shown in the figure. They are 3.0 m apart and both are playing a 686 Hz tone in phase. Part A As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? The room temperature is 20 degrees C. Express your answer numerically using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas

Answer 1

L = 3.8 m

Step-by-step explanation:

As we know that the frequency of sound is given as

`f = 686 Hz`

speed of the sound is given as

`v = 332 + 0.6 t`

`v = 332 + (0.6 * 20)`

`v = 344 m/s`

now we have wavelength of sound is given as

`\lambda = (v)/(f)`

`\lambda = (344)/(686)`

`\lambda = 0.50 m`

now we have path difference at initial position given as

`\Delta L = √(L^2 + d^2) - L`

`\Delta L = √(3^2 + 2.5^2) - 2.5`

`\Delta L = 3.9 - 2.5 = 1.4 m`

now we know that for minimum sound intensity we have

`\Delta L = (2N + 1)/(2)\lambda`

`\Delta L = (2N + 1)/(2)(0.50)`

so we have

N = 2

`\Delta L = 1.25 m`

so we have

`√(2.5^2 + L^2) - L = 1.25`

`2.5^2 + L^2 = L^2 + 1.25^2 + 2.5L`

`L = 1.875 m`

Now for N = 1

`\Delta L = 0.75 m`

so we have

`√(2.5^2 + L^2) - L = 0.75`

`2.5^2 + L^2 = L^2 + 0.75^2 + 1.5L`

`L = 3.8 m`

so the next minimum intensity will be at L = 3.8 m