Thank you for visiting A 1 70 meter string is tied to a 170 Hz sinusoidal oscillator at point P and runs over a support at point Q The. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The linear density of the string in grams per meter is 150 g/m.
The linear density of a string can be calculated by considering the factors involved in the formation of standing waves. In this scenario, we have a 1.70 m string tied to a 170 Hz sinusoidal oscillator at points P and
In this scenario, the length of the string is not given, so we need to consider the relationship between the frequency of the oscillator and the length of the string. The frequency of the oscillator is 170 Hz.
When a standing wave is formed on a string, there must be an integral number of half-wavelengths fitting into the length of the string. Since the amplitude of motion is negligible at points P and Q, they can be treated as nodes. This means that the length of the string must be equal to an odd number of half-wavelengths.
From the given information, we know that the standing wave appears when the mass of the hanging block is 399.8 g or 899.6 g. Let's analyze these two cases separately.
Case 1: Mass of the hanging block is 399.8 g
In this case, an odd number of half-wavelengths must fit into the length of the string. Since the amplitude is negligible at points P and Q, we can consider the distance between P and Q as half a wavelength.
Let's assume that the length of the string is L. Therefore, the distance between P and Q is L/2.
We can calculate the wavelength (λ) using the formula:
λ = 2(L/2)
λ = L
The speed of the wave on the string (v) can be calculated using the formula:
v = fλ
v = (170 Hz)(L)
The linear density (μ) of the string is given by the formula:
μ = (m/L)
where m is the mass of the string.
Since the amplitude of the motion is negligible, the tension in the string is constant. Therefore, the speed of the wave is also constant for different masses.
Now, let's consider Case 2: Mass of the hanging block is 899.6 g
In this case, an even number of half-wavelengths must fit into the length of the string. Again, we can assume the distance between P and Q as half a wavelength.
Using similar calculations as in Case 1, we find that:
v = (170 Hz)(L)
Since the speed of the wave is the same in both cases, the linear densities of the string in both cases should also be the same.
Therefore, the linear density of the string is the same for both cases and can be calculated by substituting the values into the formula:
μ = (m/L)
μ = (899.6 g / L) = (399.8 g / L)
Since the linear density is the same for both masses, we can set up the following equation:
(899.6 g / L) = (399.8 g / L)
Solving this equation, we find that:
L = 150 cm = 1.5 m
So, the linear density of the string is:
μ = (399.8 g / 1.5 m) = (899.6 g / 1.5 m)
Learn more about linear density in the link:
https://brainly.com/question/17594847
#SPJ11
Thank you for reading the article A 1 70 meter string is tied to a 170 Hz sinusoidal oscillator at point P and runs over a support at point Q The. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
