Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. A loud factory machine produces sound having a displacement amplitude of $1.00 \mu \mathrm{m}$, but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maximum pressure amplitude of the sound waves is limited to 10.0 Pa. Under the conditions of this factory, the bulk modulus of air is $1.42 \times 10^{5} \mathrm{Pa}$. What is the highest frequency sound to which this machine can be adjusted without exceeding the prescribed limit? Is this frequency audible to the workers?

A normally distributed random variable X has a mean of 90. Given that the probability $\mathrm{P}(X<85) \approx 0.16 :$ a. find the proportion of scores between 90 and 95, i.e., find P(90 < X < 95) b. find an estimate of the standard deviation for the random variable X.

The air temperature over a lake decreases linearly with height after sunset, since air cools faster than water. If the temperature at the surface is 25.00$^{\circ} \mathrm{C}$ and the temperature at a height of 300.0 m is 5,000$^{\circ} \mathrm{C}$, how long does it take sound to rise 300.0 m directly upward? [Hint: Use Eq. $v=\sqrt{\frac{\gamma R T}{M}}$ and integrate.]

The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 $s^{- 1}$ and the highest frequency of a piccolo is $1.5 \times 10^4 s^{- 1}$. Find the difference in wavelength between these two sounds.

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. You live on a busy street, but as a music lover, you want to reduce the traffic noise. (a) If you install special sound reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity (in $W/m^{2}$)? (b) If, instead, you reduce the intensity by half, what change (in dB) do you make in the sound intensity level?

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. What must be the stress (F/A) in a stretched wire of a material whose Young’s modulus is Y for the speed of longitudinal waves to equal 30 times the speed of transverse waves?

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. The shock-wave cone created by a space shuttle at one instant during its reentry into the atmosphere makes an angle of $58.0^{\circ}$ with its direction of motion. The speed of sound at this altitude is 331 m/s. (a) What is the Mach number of the shuttle at this instant, and (b) how fast (in m/s and in mi/h) is it traveling relative to the atmosphere? (c) What would be its Mach number and the angle of its shock-wave cone if it flew at the same speed but at low altitude where the speed of sound is 344 m/s?

You are measuring the frequency dependence of the average power $P_{\text {av }}$ transmitted by traveling waves on a wire. In your experiment you use a wire with linear mass density $3.5 \mathrm{~g} / \mathrm{m}$. For a transverse wave on the wire with amplitude $4.0 \mathrm{~mm}$, you measure $P_{\mathrm{av}}$ (in watts) as a function of the frequency $f$ of the wave (in $\mathrm{Hz}$ ). You have chosen to plot $P_{\mathrm{av}}$ as a function of $f^2$ . Explain why values of $P_{\text {av }}$ plotted versus $f^2$ should be well fit by a straight line.

A string or rope will break apart if it is placed under too much tensile stress $\text {Tensile stress}=\frac{F_{\perp}}{A}$. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density $7800 \mathrm{kg} / \mathrm{m}^{3}$ and will break if the tensile stress exceeds $7.0 \times 10^{8} \mathrm{N} / \mathrm{m}^{2}$. You want to make a guitar string from 4.0 g of this type of steel. In use, the guitar string must be able to withstand a tension of 900 N without breaking. Your job is to determine (a) the maximum length and minimum radius the string can have; (b) the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.

You have a rubber band whose relaxed length is 8.5 cm. You hang a coffee cup, whose mass is 330 g, from the rubber band, which stretches to a length of 14 cm. Consider the rubber band to be a single spring. (a) What is the stiffness of the rubber band?

Scale length is the length of the part of a guitar string that is free to vibrate. A standard value of scale length for an acoustic guitar is 25.5 in. The frequency of the fundamental standing wave on a string is determined by the string’s scale length, tension, and linear mass density. The standard frequencies f to which the strings of a six-string guitar are tuned are given in the table: "

$$\begin{matrix} \text{String} & \text{E2} & \text{A2} & \text{D3} & \text{G3} & \text{B3} & \text{E4}\\\text{f (Hz)} & \text{82.4} & \text{110.0} & \text{146.8} & \text{196.0} & \text{246.9} & \text{329.6}\\\end{matrix}$$

" Assume that a typical value of the tension of a guitar string is 78.0 N (although tension varies somewhat for different strings). (a) Calculate the linear mass density $\mu$(in g/cm) for the E2, G3, and E4 strings. (b) Just before your band is going to perform, your G3 string breaks. The only replacement string you have is an E2. If your strings have the linear mass densities calculated in part (a), what must be the tension in the replacement string to bring its fundamental frequency to the G3 value of 196.0 Hz?

A vibrating string 50 cm long is under a tension of 1 N. The results from five successive stroboscopic pictures are shown in the given figure. The strobe rate is set at 5000 flashes per minute, and observations reveal that the maximum displacement occurred at flashes 1 and 5 with no other maxima in between. What is the mass of this string?

A thin string $2.50$ m in length is stretched with a ten- sion of $90.0 \mathrm{~N}$ between two supports. When the string vibrates in its first overtone, a point at an antinode of the standing wave on the string has an amplitude of $3.50$ cm and a maximum transverse speed of $28.0$ m$/$s.
(b) What is the magnitude of the maximum transverse acceleration of this point on the string?

You are exploring a newly discovered planet. The radius of the planet is $7.20 \times 10^{7} \mathrm{m}$. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0600 s for a transverse pulse to travel from the lower end to the upper end of the string. On earth, for the same string and lead weight, it takes 0.0390 s for a transverse pulse to travel the length of the string. The weight of the string is small enough that its effect on the tension in the string can be neglected. Assuming that the mass of the planet is distributed with spherical symmetry, what is its mass?