Wave Interference Practice Problems

Two speakers are placed facing an audience. The speakers are playing a tone in phase with each other at a wavelength of 0.85 m. A member of the audience has the position shown. Determine the path difference for the waves emitted by the speakers. 

Mobile phone network towers P and Q are separated by 375 m. Tower P is located left of tower Q. Their antennas are radiating in phase at identical frequencies. A mobile phone is located to the left of antenna P at point R, 1.2 km from the tower on the axis connecting the two antennas. Mobile networks have various bands with different frequencies and wavelengths. Assuming the bands can have any frequency value, determine the largest wavelength that produces constructive interference at point R. 

Digital television broadcast towers F and G are 257 m apart. Tower F is located left of tower G. Their antennas radiate in phase at the same frequency. A TV antenna is located at point H, 1 km to the right of antenna G on the axis connecting the two antennas. TV networks broadcast at various frequencies called channels. Assuming a channel can have any frequency, and similarly, the wavelength, determine the longest wavelength of a channel that will cause destructive interference at point H. 

Two speakers in an open field are separated by 20.0 m. A tune of 550 Hz from the same source is channeled to the speakers. The temperature is quite high, raising the speed of sound in air to 349 m/s. A recording microphone is located at the center of the two speakers. What distance measured from the midpoint of the two speakers will the microphone detect a first maximum gain of the sound? 

Two speakers on a roadshow truck are 11.0 m apart. A notification of frequency 850 Hz and in the same phase is playing from the speakers. The speed of sound in the air at that instant is 346 m/s. The reflections from the walls of the truck are negligible. A programmer is standing at the center of the two speakers listening carefully while directly facing one of the speakers. This orientation means both ears have the same distance measured from both speakers. Does the programmer detect constructive or destructive interference? Explain?

A 75 inch  LED TV has left and right stereo speakers separated by 1.50 m. The speakers, which are run by the same sound card inside the TV are beeping the same notification tone. The microphone on a recording smartphone is placed perpendicularly and 0.8 m directly in front of one of the speakers. Determine all frequencies between 20 Hz and 1.5 kHz that cause constructive interference at the location of the microphone.

A vehicle (at rest) is fitted with two sirens that are 2.2 m apart. The sirens are operated by the same circuitry, emitting pure sine waves that are in phase. A point S lies 1.1 m on one side measured from the sirens. For sound waves traveling straight from the siren to point S, calculate the least frequency that causes destructive interference at point S.

Two identical alarm speakers connected to the same circuit are fitted to a building. They are separated by 5.0 m. Point P is located 2.0 m from alarm D on the axis connecting the two speakers. If pure sine waves emitted by both alarms are in phase and move straight to point P, determine the least frequency capable of causing constructive interference at point P.

A radio with two detached speakers is tuned to a radio station playing an alert tone at 1050 Hz. The speakers are initially placed at the same point, 3.20 m away from a listener. One speaker is moved backward from the listener. What distance x between the two speakers will create destructive interference for the second time at the listener's position?