Correct answer Carries: 4.
Wrong Answer Carries: -1.
A string fixed at both ends vibrates in its second harmonic with a frequency of 80 Hz. If its length is 1 m, what is the wave speed?
For fixed ends: \( v_n = \frac{n v}{2L} \).
Second harmonic (\( n = 2 \)): \( 80 = \frac{2 \times v}{2 \times 1} \).
\( 80 = \frac{v}{1} \Rightarrow v = 80 \, \text{m/s} \).
A transverse wave on a string has a tension of 90 N and a linear mass density of 0.01 kg/m. What is the frequency if the wavelength is 1.5 m?
Speed: \( v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{90}{0.01}} = \sqrt{9000} \approx 94.87 \, \text{m/s} \).
Frequency: \( v = \frac{v}{\lambda} = \frac{94.87}{1.5} \approx 63.25 \, \text{Hz} \).
A stationary wave on a string fixed at both ends has a wavelength of 0.4 m and a frequency of 150 Hz. What is the wave speed?
Speed: \( v = v \lambda = 150 \times 0.4 = 60 \, \text{m/s} \).
What is the phase change when a longitudinal wave reflects off a rigid boundary?
For a longitudinal wave, a rigid boundary (fixed end) causes a compression to reflect as a compression, resulting in no phase change (0 radians), unlike transverse waves which invert.
Which characteristic of a wave remains constant when it travels from one medium to another with different properties?
When a wave crosses a boundary between media, its speed and wavelength change due to differing medium properties, but frequency remains constant as it is determined by the source.
A transverse wave on a string has a tension of 200 N and a linear mass density of 0.04 kg/m. What is the wavelength if the frequency is 25 Hz?
Speed: \( v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{200}{0.04}} = \sqrt{5000} \approx 70.71 \, \text{m/s} \).
Wavelength: \( \lambda = \frac{v}{v} = \frac{70.71}{25} \approx 2.83 \, \text{m} \).
What is the primary physical quantity that remains constant for a wave reflecting off a boundary within the same medium?
Reflection within the same medium preserves the wave’s frequency, as it depends on the source, while speed, wavelength, and amplitude may adjust based on boundary conditions.
A wave is described by \( y(x, t) = 0.01 \sin (40x - 80t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the frequency of the wave?
Compare with \( y = a \sin (kx - \omega t) \), \( \omega = 80 \, \text{rad/s} \).
Frequency: \( v = \frac{\omega}{2\pi} = \frac{80}{2\pi} \approx 12.73 \, \text{Hz} \).
A stationary wave on a string fixed at both ends has a frequency of 80 Hz and a wave speed of 32 m/s. What is the length of the string?
Fundamental: \( v_1 = \frac{v}{2L} \).
\( 80 = \frac{32}{2L} \Rightarrow 2L = \frac{32}{80} \Rightarrow 2L = 0.4 \Rightarrow L = 0.2 \, \text{m} \).
A pipe closed at one end has a length of 0.4 m and a speed of sound of 320 m/s. What is its fundamental frequency?
For closed pipe: \( v_1 = \frac{v}{4L} \).
\( v_1 = \frac{320}{4 \times 0.4} = \frac{320}{1.6} = 200 \, \text{Hz} \).
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