A sinusoidal wave moving along a string is shown twice in Figure 16-33, as crest A travels in the positive direction of an x axis by distance d = 6.0 cm in 4.0 ms . The tick marks along the axis are separated by 10 cm ; height H = 6.00mm If the wave equation is of the form, $\mathit{y}\left(x,t\right)\mathbf{=}{\mathit{y}}_{\mathbf{m}}\mathit{s}\mathit{i}\mathit{n}\left(kx+\omega t\right)$

(a) What is ${\mathit{y}}_{\mathbf{m}}$ ,

(b) What is k ,

(c) What is $\mathit{\omega }$ , and

(d) What is the correct choice of sign in front of $\mathit{\omega }$?

The following four waves are sent along strings with the same linear densities (x is in meters and t is in seconds). Rank the waves according to (a) their wave speed and (b) the tension in the strings along which they travel, greatest first:

(1)${\mathit{Y}}^{\mathbf{1}}\mathbf{=}\mathbf{\left(}\mathbf{3}\mathit{m}\mathit{m}\mathbf{\right)}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{3}\mathit{t}\mathbf{)}\mathbf{,}$ (3)${\mathit{y}}^{\mathbf{3}}\mathbf{=}\mathbf{\left(}\mathbf{1}\mathit{m}\mathit{m}\mathbf{\right)}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{(}\mathbf{4}\mathit{x}\mathbf{-}\mathit{t}\mathbf{)}$ ,

(2) ${\mathit{y}}^{\mathbf{2}}\mathbf{=}\mathbf{\left(}\mathbf{6}\mathit{m}\mathit{m}\mathbf{\right)}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{(}\mathbf{2}\mathit{x}\mathbf{-}\mathit{t}\mathbf{)}$, (4) ${\mathit{y}}^{\mathbf{4}}\mathbf{=}\mathbf{\left(}\mathbf{2}\mathit{m}\mathit{m}\mathbf{\right)}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{2}\mathit{t}\mathbf{)}$.

The speed of electromagnetic waves (which include visible light, radio, and x rays) in vacuum is $\mathbf{30}\mathit{x}{\mathbf{10}}^{\mathbf{8}}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}$. (a) Wavelengths of visible light waves range from about 700 nm in the violet to about 700 nm in the red. What is the range of frequencies of these waves? (b)The range of frequencies for shortwave radio (for example, FM radio and VHF television) is 1.5 to 300 MHz . What is the corresponding wavelength range? (c) X-ray wavelengths range from about 5.0 nm to about $\mathbf{1}\mathbf{.}\mathbf{0}\mathit{x}{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{}\mathit{n}\mathit{m}$ . What is the frequency range for x rays?

A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (Figure). The waves are of two types: transverse waves traveling at ${\mathit{v}}_{\mathbf{t}}\mathbf{=}\mathbf{50}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$ and longitudinal waves traveling at ${\mathit{v}}_{\mathbf{t}}\mathbf{=}\mathbf{50}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$. If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference localid="1657274843608" $\mathit{t}$ in the arrival times of the waves at its leg nearest the beetle. If localid="1661230422984" $\mathbf{∆}\mathit{t}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{ms}$, what is the beetle’s distance?

One of the harmonic frequencies for a particular string under tension is 325 Hz .The next higher harmonic frequency is 390 Hz . What harmonic frequency is next higher after the harmonic frequency 195 Hz?

If you set up the seventh harmonic on a string, (a) how many nodes are present, and (b) is there a node, antinode, or some intermediate state at the midpoint? If you next set up the sixth harmonic, (c) is its resonant wavelength longer or shorter than that for the seventh harmonic, and (d) is the resonant frequency higher or lower?