Exam 18: Superposition and Interference

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 *10-3 kg/m and a tension of 80 N when both ends are fixed in place.

Which of the following wavelengths could NOT be present as a harmonic on a 2 m long string?

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 frequency of:

Superposition of waves can occur:

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in:

Two harmonic waves are described by: $y_{1}=(3 \mathrm{~m}) \sin \left(\frac{4}{\mathrm{~m}} x-\frac{700}{\mathrm{~s}} t\right)$ $y_{2}=(3 \mathrm{~m}) \sin \left(\frac{4}{\mathrm{~m}} x-\frac{700}{\mathrm{~s}} t-2\right)$ What is the amplitude of the resultant wave?

Two tuning forks with frequencies 264 and 262 Hz produce 'beats'. What is the beat frequency (in Hz)?

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the fundamental frequency?

A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?

Two waves are described by: y1 = 6 cos 180t and y2 = 6 cos 186t, (both in metres).With what angular frequency does the maximum amplitude of the resultant wave vary with time?

As shown below, a garden room has three walls, a floor and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When travelling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is:

A string with a fixed frequency vibrator at one end is undergoing resonance with 4 antinodes when under tension T1. When the tension is slowly increased the resonance condition disappears until tension T2 is reached, there being no resonances occurring between these two tensions. How many antinodes are there in this new resonance?

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the wavelength (in cm) of the first harmonic?

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in:

The superposition of two waves and $y_{2}=(0.006 \mathrm{~cm}) \cos \left[2 \pi\left(\frac{150}{\mathrm{~s}} t\right)\right]$ at the location x = 0 in space results in:

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (fc = 261.6 Hz)?

Two pulses are travelling towards each other at 10 cm/s on a long string at t = 0 s, as shown below. Which diagram below correctly shows the shape of the string at 0.5 s?

The figure below shows the positions of particles in a longitudinal standing wave. One-quarter period later the particle distribution is shown in:

Tuning forks #1, #2, and #3 each have slightly different frequencies. When #1 and #2 are sounded together, a beat frequency of 3 Hz results. When #2 and #3 are sounded together, a beat frequency of 5 Hz results. If the frequency of #1 is 100 Hz, which of the following cannot be the frequency of #3?

Two speakers in an automobile emit sound waves that are in phase at the speakers. One speaker is 40 cm ahead of and 30 cm to the left of the driver's left ear. The other speaker is 50 cm ahead of and 120 cm to the right of the driver's right ear. Which of the following wavelengths is(are) in phase at the left ear for the speaker on the left and the right ear for the speaker on the right?