A sound wave has a frequency of `2 kHz` and wavelength `35 cm`. How long will it take to travel `1.5 km` ?

Explanation

To solve the problem step by step, we will follow a systematic approach:

### Step 1: Convert the Wavelength to Meters
The given wavelength is 35 cm. We need to convert this to meters.
\[ \text{Wavelength} = 35 \text{ cm} = \frac{35}{100} \text{ m} = 0.35 \text{ m} \]

### Step 2: Convert the Distance to Meters
The distance given is 1.5 km. We will convert this to meters as well.
\[ \text{Distance} = 1.5 \text{ km} = 1.5 \times 1000 \text{ m} = 1500 \text{ m} \]

### Step 3: Convert the Frequency to Hertz
The frequency is given as 2 kHz. We need to convert this to Hertz.
\[ \text{Frequency} = 2 \text{ kHz} = 2 \times 1000 \text{ Hz} = 2000 \text{ Hz} \]

### Step 4: Calculate the Velocity of the Sound Wave
We can calculate the velocity of the sound wave using the formula:
\[ v = \mu \times \lambda \]
Where \( \mu \) is the frequency and \( \lambda \) is the wavelength.
\[ v = 2000 \text{ Hz} \times 0.35 \text{ m} = 700 \text{ m/s} \]

### Step 5: Calculate the Time Taken to Travel the Distance
Now, we can find the time taken to travel the distance using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} \]
Substituting the values we have:
\[ \text{Time} = \frac{1500 \text{ m}}{700 \text{ m/s}} = \frac{1500}{700} \text{ s} = \frac{15}{7} \text{ s} \approx 2.14 \text{ s} \]

### Final Answer
The time taken for the sound wave to travel 1.5 km is approximately **2.14 seconds**.

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