Question

practice

1. if the temperature of the air in your region is 32 °c, what is the speed of sound in at that temperature? ans: 351 m/s
2. if the speed of sound near you is 333 m/s, what is the ambient temperature? ans: 2.64 °c
3. if the speed of sound near you is 350 m/s, what is the ambient temperature? ans: 31 °c

Explanation:

Problem 1

Step1: Identify the formula

The formula for the speed of sound \( v \) in air is \( v = 331.4\,\text{m/s} + (0.606\,\text{m/s/}^\circ\text{C}) \times T \), where \( T \) is the temperature in \( ^\circ\text{C} \).

Step2: Substitute the temperature value

Given \( T = 32^\circ\text{C} \), substitute into the formula:
\( v = 331.4 + (0.606 \times 32) \)

Step3: Calculate the product

First, calculate \( 0.606 \times 32 \):
\( 0.606 \times 32 = 19.392 \)

Step4: Add to the initial speed

Then, add to \( 331.4 \):
\( v = 331.4 + 19.392 = 350.792 \approx 351\,\text{m/s} \) (rounded to a reasonable precision)

Step1: Start with the speed of sound formula

The formula is \( v = 331.4 + 0.606T \). We need to solve for \( T \) when \( v = 333\,\text{m/s} \).

Step2: Rearrange the formula

Subtract \( 331.4 \) from both sides:
\( v - 331.4 = 0.606T \)
Then, divide both sides by \( 0.606 \):
\( T = \frac{v - 331.4}{0.606} \)

Step3: Substitute \( v = 333 \)

Substitute \( v = 333 \) into the rearranged formula:
\( T = \frac{333 - 331.4}{0.606} \)

Step4: Calculate the numerator

First, calculate \( 333 - 331.4 = 1.6 \)

Step5: Divide to find \( T \)

Then, divide by \( 0.606 \):
\( T = \frac{1.6}{0.606} \approx 2.64^\circ\text{C} \)

Step1: Use the speed of sound formula

The formula is \( v = 331.4 + 0.606T \). Solve for \( T \) when \( v = 350\,\text{m/s} \).

Step2: Rearrange the formula

\( T = \frac{v - 331.4}{0.606} \)

Step3: Substitute \( v = 350 \)

Substitute \( v = 350 \):
\( T = \frac{350 - 331.4}{0.606} \)

Step4: Calculate the numerator

\( 350 - 331.4 = 18.6 \)

Step5: Divide to find \( T \)

\( T = \frac{18.6}{0.606} \approx 30.69 \approx 31^\circ\text{C} \) (rounded to a reasonable precision)

Answer:

The speed of sound is \( \boldsymbol{351\,\text{m/s}} \)

Problem 2