While testing speakers for a concert, Tomás sets up two speakers to produce sound waves at the same frequency, which is between

Question

4 years ago

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While testing speakers for a concert, Tomás sets up two speakers to produce sound waves at the same frequency, which is between

100 Hz and 150 Hz. The two speakers vibrate in phase with each other. He notices that when he listens at certain locations, the sound is very soft (a minimum intensity compared to nearby points). One such point is 26.1 m from one speaker and 37.3 m from the other. (The speed of sound in air is 343 m/s.)

Physics

2 answers:

andrew11 [14] · Answer 1 · 2022-01-15T10:00:38+03:00

Answer:

frequencies are 106.5 Hz and 138.30 Hz

Explanation:

The difference in path length is 37.3 - 26.1 m = 11.2 m

For cancellation, Above given length must be a odd number of half-wavelengths.

Minimum wavelength is ( 343 m/s / 150 Hz) = 2.29 m

Maximum wavelength is (343 m/s / 100 Hz) = 3.43 m

11.2 / 2.5 = 4.48 m => too long

11.2 / 3.5 = 3.2 m => ok

11.2 / 4.5 = 2.48 m => ok

11.2 / 5.5 = 2.03 m => too short

so we have following possible frequencies $\frac{343}{3.2} = 106.5 Hz$

$\frac{343}{2.48} = 138.30 Hz$

vlabodo [156] · Answer 2 · 2022-01-15T12:08:53+03:00

Answer:

107.18Hz

138.3 Hz

Explanation:

While testing speakers for a concert, Tomás sets up two speakers to produce sound waves at the same frequency, which is between 100 Hz and 150 Hz. The two speakers vibrate in phase with each other. He notices that when he listens at certain locations, the sound is very soft (a minimum intensity compared to nearby points). One such point is 26.1 m from one speaker and 37.3 m from the other. (The speed of sound in air is 343 m/s.)

Assumption:What are the possible frequencies of

the sound waves coming from the speakers? could be the concluding part of the question

Definition of terms: Frequency is the number of oscillation made in one seconds. unit is Hertz

Wavelength is the ratio of velocity to frequency.

The difference in path length is 37.3 - 26.1m = 11.2m

The wavelength at minimum under consideration is 343m/s / 150Hz = 2.29m

The maximum wavelength is 343m/s / 100Hz = 3.43m

11.2 / 2.5 = 4.48 m => too long

11.2 / 3.5 = 3.2 m => good

11.2/ 4.5 = 2.48 m => ok

11.2 / 5.5 = 2.03m => too short

the minim um and maximum frequencies are: