A row of seats is parallel to a stage at a distance of 8.70 m from it. At the center and front of the stage is a diffraction horn loudspeaker that has a width of 7.50 cm. The speaker is playing a tone at a frequency of 9600 Hz . The speed of sound is 344 m/s.
a. What is the separation between two seats, located on opposite sides of the center of the row, at which the tone cannot be heard?
can you explain to me how to attempt this question step by step (do not solve). Thanks
figured it out nvm
To attempt this question, you can use the principles of diffraction and the concept of the minimum audible angle to find the separation between the two seats at which the tone cannot be heard. Here are the steps to follow:
1. Understand the concept of diffraction: Diffraction is the bending of waves around obstacles or through openings. In this case, the sound waves from the speaker will diffract around the seats and reach the listener's ears.
2. Determine the wavelength of the sound wave: The wavelength (λ) of a sound wave can be calculated using the formula λ = v / f, where v is the speed of sound (given as 344 m/s) and f is the frequency of the tone (given as 9600 Hz). Calculate the wavelength using this formula.
3. Calculate the angular spread of the sound wave: The angular spread (θ) can be determined using the formula θ = λ / W, where λ is the wavelength of the sound wave (obtained in the previous step) and W is the width of the diffraction horn loudspeaker (given as 7.50 cm). Calculate the angular spread using this formula.
4. Understand the concept of the minimum audible angle: The minimum audible angle is the smallest angular separation between two sources from which a listener can distinguish between the two sources. If the angular separation between the two seats is smaller than the minimum audible angle, the tone will not be audible.
5. Find the minimum audible angle: The minimum audible angle depends on various factors such as the frequency of the sound, distance from the source, and individual hearing capabilities. You can refer to standard references or research articles to find the minimum audible angle for a tone of 9600 Hz.
6. Calculate the separation between two seats: Once you have the minimum audible angle, you can use trigonometry to calculate the physical separation between two seats at which the tone cannot be heard. The separation can be found using the formula separation = distance × tan (min audible angle).
By following these steps, you can attempt to find the separation between two seats at which the tone cannot be heard without actually solving the problem.