The speed of sound in air at 0 degree C is 332 m/s. If it increases at the rate of 0.6 m/s per degree, what will be the temperature when the velocity has increased to 344 m/s?
Understand the Problem
The question is asking to find the temperature at which the speed of sound in air reaches 344 m/s, given that the speed at 0°C is 332 m/s and it increases by 0.6 m/s for every degree Celsius increase in temperature. We need to determine the temperature increase required to reach the new speed, then add that increase to the initial temperature to find the final temperature.
Answer
$20 \, \text{°C}$
Answer for screen readers
$20 , \text{°C}$
Steps to Solve
- Determine the required increase in speed.
We need to find the difference between the desired speed (344 m/s) and the initial speed (332 m/s).
$ \text{Speed increase} = 344 , \text{m/s} - 332 , \text{m/s} = 12 , \text{m/s} $
- Calculate the required temperature increase.
Since the speed increases by 0.6 m/s for every 1°C increase, we can find the temperature increase by dividing the required speed increase by the rate of speed increase per degree Celsius.
$ \text{Temperature increase} = \frac{12 , \text{m/s}}{0.6 , \text{m/s/°C}} = 20 , \text{°C} $
- Calculate the final temperature.
The initial temperature is 0°C. Add the temperature increase to the initial temperature to find the final temperature.
$ \text{Final temperature} = 0 , \text{°C} + 20 , \text{°C} = 20 , \text{°C} $
$20 , \text{°C}$
More Information
The speed of sound in air is affected by temperature, increasing as the temperature rises. This is why musical instruments that rely on air columns, like flutes or organ pipes, may sound slightly different in tune on a hot day compared to a cold day!
Tips
A common mistake is to forget to consider the initial temperature. It's important to add the temperature increase to the initial temperature to find the final temperature. In this case, the initial temperature was 0°C, making things simple, but in other similar problems, this step is crucial.
AI-generated content may contain errors. Please verify critical information
