The speed of sound in air at 20°C is 344 m/s. (a) What is the wavelength of a sound wave with a frequency of 784 Hz, corresponding to the note G₅ on a piano, and how many milliseconds does each vibration take? (b) What is the wavelength of a sound wave one octave higher (twice the frequency) than the note in part (a)?

Threshold of Pain. You are investigating the report of a UFO landing in an isolated portion of New Mexico, and you encounter a strange object that is radiating sound waves uniformly in all directions. Assume that the sound comes from a point source and that you can ignore reflections. You are slowly walking toward the source. When you are 7.5 m from it, you measure its intensity to be 0.11 W/m². An intensity of 1.0 W/m² is often used as the 'threshold of pain.' How much closer to the source can you move before the sound intensity reaches this threshold?

A jet plane at takeoff can produce sound of intensity 10.0 W/m² at 30.0 m away. But you prefer the tranquil sound of normal conversation, which is 1.0 μW/m². Assume that the plane behaves like a point source of sound. (a) What is the closest dis-tance you should live from the airport runway to preserve your peace of mind? (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? (c) What power of sound does the jet produce at takeoff?

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is $y(x,t)=\left(2.30\operatorname{mm)}\cos[\left(16.98\text{ }rad/m\right)x+(742\text{ }rad/s\right)t]$. Being more practical, you measure the rope to have a length of $1.35\text{ m}$ and a mass of $0.00338\operatorname{kg}$. You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength.

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is $y(x,t)=\left(2.30\operatorname{mm)}\cos[\left(16.98\text{ }rad/m\right)x+(742\text{ }rad/s\right)t]$. Being more practical, you measure the rope to have a length of $1.35\text{ m}$ and a mass of $0.00338\operatorname{kg}$. You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is $y(x,t)=(2.30\mathrm{mm)}\cos [\left(16.98rad/m\right)x+\left(742rad/s\right)t]$. Being more practical, you measure the rope to have a length of $1.35\text{ m}$ and a mass of $0.00338\mathrm{kg}$. You are then asked to determine the following: (f) tension in the rope; (g) average power transmitted by the wave.

Energy Output. By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is 0.026 W/m² at a distance of 4.3 m from the source. What is the intensity at a distance of 3.1 m from the source?

Energy Output. By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is 0.026 W/m² at a distance of 4.3 m from the source. How much sound energy does the source emit in one hour if its power output remains constant?

A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the fundamental?

A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the second overtone?

A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the fourth harmonic?

A wire with mass 40.0 g is stretched so that its ends are tied down at points 80.0 cm apart. The wire vibrates in its fundamental mode with frequency 60.0 Hz and with an amplitude at the antinodes of 0.300 cm. What is the speed of propagation of transverse waves in the wire?

A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire is 0.400 m long and has a mass of 3.00 g. What is the frequency of its fundamental mode of vibration?

CALC. A thin, taut string tied at both ends and oscillating in its third harmonic has its shape described by the equation $y(x,t)=\left(5.60\text{ cm}\right)\sin \left[\right(0.0340\text{ rad/cm}\left)x\right]\sin \left[\right(50.0\text{ rad/s}\left)t\right]$, where the origin is at the left end of the string, the $x$-axis is along the string, and the $y$-axis is perpendicular to the string. Draw a sketch that shows the standing-wave pattern.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin \left[\right(32.5\text{ rad/m}\left)x\right]\sin \left[\right(754\text{rad/s}\left)t\right]$. For the two traveling waves that make up this standing wave, find the amplitude.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin[(32.5\text{ rad/m})x]\sin[(754\text{rad/s})t]$. For the two traveling waves that make up this standing wave, find the wavelength.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin[(32.5\text{ rad/m})x]\sin[(754\text{rad/s})t]$. For the two traveling waves that make up this standing wave, find the frequency.

The wave function of a standing wave is $y(x,t)=4.44\text{ mm}\sin[(32.5\text{ rad/m})x]\sin[(754\text{rad/s})t]$. For the two traveling waves that make up this standing wave, find the wave speed.

One string of a certain musical instrument is 75.0 cm long and has a mass of 8.75 g. It is being played in a room where the speed of sound is 344 m/s. (a) To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.765 m? (Assume that the break-ing stress of the wire is very large and isn't exceeded.) (b) What frequency sound does this string produce in its fundamental mode of vibration?

A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed $v$, frequency $f$, amplitude $A$, and wavelength $\lambda$. Calculate the maximum transverse velocity and maximum transverse acceleration of points located at (i) $x = λ/2$, (ii) $x = λ/4$, and (iii) $x = λ/8$, from the left-hand end of the string.

A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed $v$, frequency $f$, amplitude $A$, and wavelength $\lambda$. What is the amplitude of the motion at the points located at (i) $x=\lambda /2$, (ii) $x=\lambda /4$, and (iii) $x=\lambda /8$, from the left-hand end of the string?

A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed $v$, frequency $f$, amplitude $A$, and wavelength $\lambda$. How much time does it take the string to go from its largest upward displacement to its largest downward displacement at the points located at (i) $x = λ/2$, (ii) $x = λ/4$, and (iii) $x = λ/8$, from the left-hand end of the string.