A sinusoidal wave is traveling on a string with speed 149 cm/s. The displacement of the particles of the string at x = 20 cm is found to vary with time according to the equation y = (5.9 cm) sin[0.86 - (6.4 s)t). The linear density of the string is 1.8 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form y(x,t) = ym sin(kx - wt), what are (c) ym, (d) k, and (e) w, and (f) the correct choice of sign in front of w? (g) What is the tension in the string?
A sinusoidal wave is traveling on a string with speed 149 cm/s. The displacement of the particles of the string at x = 20 cm is found to vary with time according to the equation y = (5.9 cm) sin[0.86 - (6.4 s)t). The linear density of the string is 1.8 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form y(x,t) = ym sin(kx - wt), what are (c) ym, (d) k, and (e) w, and (f) the correct choice of sign in front of w? (g) What is the tension in the string?
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![**Wave on a String Problem**
A sinusoidal wave is traveling on a string with a speed of 149 cm/s. The displacement of the particles of the string at \( x = 20 \, \text{cm} \) is found to vary with time according to the equation:
\[ y = (5.9 \, \text{cm}) \sin[0.86 - (6.4 \, \text{s}^{-1}) t]. \]
The linear density of the string is \( 1.8 \, \text{g/cm} \).
**Questions:**
(a) What is the frequency of the wave?
(b) What is the wavelength of the wave?
If the wave equation is of the form:
\[ y(x,t) = y_m \sin(kx - \omega t), \]
what are:
(c) \( y_m \)
(d) \( k \)
(e) \( \omega \)
(f) The correct choice of sign in front of \( \omega \)?
(g) What is the tension in the string?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18d6601c-1264-4982-ae9d-82e3a3c3c6e6%2F6d65b3b8-0a4c-4a1d-b4cc-2a716372505e%2Fe1ffrtr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Wave on a String Problem**
A sinusoidal wave is traveling on a string with a speed of 149 cm/s. The displacement of the particles of the string at \( x = 20 \, \text{cm} \) is found to vary with time according to the equation:
\[ y = (5.9 \, \text{cm}) \sin[0.86 - (6.4 \, \text{s}^{-1}) t]. \]
The linear density of the string is \( 1.8 \, \text{g/cm} \).
**Questions:**
(a) What is the frequency of the wave?
(b) What is the wavelength of the wave?
If the wave equation is of the form:
\[ y(x,t) = y_m \sin(kx - \omega t), \]
what are:
(c) \( y_m \)
(d) \( k \)
(e) \( \omega \)
(f) The correct choice of sign in front of \( \omega \)?
(g) What is the tension in the string?
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