Question:

Two loudspeakers A and B are placed 3 meters apart. Source A emits a sound wave with a frequency of 500 Hz and a wavelength of 0.7 meters, while source B emits a sound wave with a frequency of 350 Hz and an unknown wavelength. A student is standing 5 meters away from loudspeaker A.

a) Calculate the speed of sound in air.

b) Determine the wavelength of the sound wave emitted by loudspeaker B.

c) Calculate the period of the sound wave emitted by loudspeaker B.

d) Calculate the time difference between hearing sound from loudspeaker A and loudspeaker B at the student's location.

Assume that the speed of sound in air is 343 m/s.

Answer:

a) To calculate the speed of sound in air, we use the formula:

speed = frequency x wavelength

For loudspeaker A, the frequency is 500 Hz, and the wavelength is 0.7 meters:

speed_A = 500 Hz x 0.7 m = 350 m/s

Therefore, the speed of sound in air is 350 m/s.

b) Given that the speed of sound in air is 350 m/s, and loudspeaker B emits a sound wave with a frequency of 350 Hz, we can use the formula speed = frequency x wavelength to find the wavelength:

350 m/s = 350 Hz x wavelength_B

Rearranging the equation gives us:

wavelength_B = 350 m/s / 350 Hz = 1 meter

Therefore, the wavelength of the sound wave emitted by loudspeaker B is 1 meter.

c) The period of a sound wave is the time it takes for one complete cycle. It can be calculated using the formula:

period = 1 / frequency

For loudspeaker B, the frequency is 350 Hz:

period_B = 1 / 350 Hz = 0.00286 s (rounded to 5 decimal places)

Therefore, the period of the sound wave emitted by loudspeaker B is approximately 0.00286 seconds.

d) To calculate the time difference between hearing sound from loudspeaker A and loudspeaker B at the student's location, we need to consider the distance between the student and each loudspeaker.

The time taken for sound to travel from loudspeaker A to the student is:

time_A = distance / speed_A = 5 m / 350 m/s = 0.0143 s

Similarly, the time taken for sound to travel from loudspeaker B to the student is:

time_B = distance / speed = 5 m / 343 m/s = 0.0146 s

The time difference is the absolute difference between these two times:

time_difference = | time_B - time_A | = | 0.0146 s - 0.0143 s | = 0.0003 s

Therefore, the time difference between hearing sound from loudspeaker A and loudspeaker B at the student's location is 0.0003 seconds.