How long would it take a sound wave to travel 150m

• rpthomps
In summary, using the given information, the time it would take a sound wave to travel 150 m over a path where the temperature rises linearly from 5 degrees to 15 degrees is 0.445 seconds. This is calculated by integrating the equation dt = dx/v and substituting the given values, resulting in a total time of 0.67 seconds. However, after correcting the lower boundary to 5 degrees, the correct answer is obtained. Additionally, the use of the formula v = d/t can also be used to calculate the distance of a thunderstorm from an observer, making Physics an exciting subject.
rpthomps

Homework Statement

The sound speed in air at 0 degrees Celsius is 331 m/s, and for temperatures within a few tens of degrees of 0 degrees celsius it increases at the rate 0.590 m/s for every degree celsius increase in temperature. How long would it take a sound wave to travel 150 m over a path where the temperature rises linearly from 5 degrees to 15 degrees at the other end?

Homework Equations

d= 150 mv=331+0.59T##T=(\frac{1}{15})x+5\\dT=\frac{1}{15}dx##

The Attempt at a Solution

##dt=\frac { dx }{ v }\\T_{ total }=\int _{ 0 }^{ 150 }{ \frac { dx }{ v } }\\=\int _{ 0 }^{ 150 }{ \frac { 15dT }{ 331+0.59T } }\\=\frac { 15 }{ 0.59 } ln(331+0.59T){ | }_{ 0 }^{ 15 }=0.67##Back of the book says .445 s

rpthomps said:

Homework Statement

The sound speed in air at 0 degrees Celsius is 331 m/s, and for temperatures within a few tens of degrees of 0 degrees celsius it increases at the rate 0.590 m/s for every degree celsius increase in temperature. How long would it take a sound wave to travel 150 m over a path where the temperature rises linearly from 5 degrees to 15 degrees at the other end?

Homework Equations

d= 150 mv=331+0.59T##T=(\frac{1}{15})x+5\\dT=\frac{1}{15}dx##

The Attempt at a Solution

##dt=\frac { dx }{ v }\\T_{ total }=\int _{ 0 }^{ 150 }{ \frac { dx }{ v } }\\=\int _{ 0 }^{ 150 }{ \frac { 15dT }{ 331+0.59T } }\\=\frac { 15 }{ 0.59 } ln(331+0.59T){ | }_{ 0 }^{ 15 }=0.67##Back of the book says .445 s
Is the initial temperature 0° ?

rpthomps
Yup, that's it. the lower boundary should be 5 degrees. When I recalculate, I get the correct answer. Thank you sir!

how thrilling is it that using a simple formula v = d/t, you can calculate how far a thunderstorm is from you! So exciting! I love Physics!

1. How is the speed of sound calculated?

The speed of sound is calculated by multiplying the frequency of the sound wave by its wavelength. The formula for calculating speed of sound is v = f x λ, where v is the speed of sound, f is the frequency, and λ is the wavelength.

2. What is the speed of sound in air?

The speed of sound in air varies depending on factors such as temperature, humidity, and altitude. However, on average, the speed of sound in dry air at room temperature is approximately 343 meters per second or 767 miles per hour.

3. Does the speed of sound change in different mediums?

Yes, the speed of sound changes in different mediums. For example, sound travels faster in solids (such as steel) than in liquids (such as water) and even slower in gases (such as air).

4. How does distance affect the speed of sound?

The distance between the source of the sound and the listener does not affect the speed of sound. However, the time it takes for the sound to travel the distance will vary depending on the speed of sound in the medium it is traveling through.

5. How long would it take a sound wave to travel 150m?

Assuming the speed of sound is constant at 343 meters per second, it would take approximately 0.44 seconds for a sound wave to travel 150 meters.

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