Exam 18: Superposition and Interference

The superposition of two waves $y_{1}=\left(2 \times 10^{-8} \mathrm{~m}\right) \sin \left[\pi\left(\frac{x}{2 \mathrm{~m}}-\frac{170}{\mathrm{~s}} t\right)\right]$ and $y_{2}=\left(2 \times 10^{-8} \mathrm{~m}\right) \sin \left[\pi\left(\frac{x}{2 \mathrm{~m}}-\frac{170}{\mathrm{~s}} t-\frac{1}{2}\right)\right]$ , results in a wave with a wavelength of:

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?

The path difference between two waves is 5 m. If the wavelength of the waves emitted by the two sources is 4 m, what is the phase difference (in degrees)?

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170 Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P?

In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is:

Two harmonic waves are described by: From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

When two organ pipes each closed at one end sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

A vertical tube one metre long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?