Open Question
(II) The wave on a string shown in Fig. 15–35 is moving to the right with a speed of 1.10 m/s.
(b) Estimate the vertical speed of point A on the string at the instant shown in Fig. 15–35.
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18. Waves & Sound
Intro to Waves
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A string with a linear mass density of is under of tension. How long would it take a wave pulse on this string to travel
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Verified step by step guidance1
First, understand that the speed of a wave on a string is determined by the tension in the string and the linear mass density. The formula for the wave speed \( v \) is given by \( v = \sqrt{\frac{T}{\mu}} \), where \( T \) is the tension and \( \mu \) is the linear mass density.
Convert the linear mass density from grams per meter to kilograms per meter, since the standard unit of mass in physics is kilograms. So, \( 1.6 \text{ g/m} = 0.0016 \text{ kg/m} \).
Substitute the given values into the wave speed formula. Here, \( T = 4.0 \text{ N} \) and \( \mu = 0.0016 \text{ kg/m} \). Calculate the wave speed \( v \) using \( v = \sqrt{\frac{4.0}{0.0016}} \).
Once you have the wave speed, use the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \) to find the time it takes for the wave pulse to travel 3.0 meters. Substitute \( \text{distance} = 3.0 \text{ m} \) and the calculated wave speed into this formula.
Calculate the time using the values from the previous steps to find how long it takes for the wave pulse to travel 3.0 meters on the string.
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