To determine the frequency of an unmarked fork in tune with a string of length 14.8 cm, let's proceed through the necessary calculations.
1. Convert the length of the string from centimeters to meters:
The length of the string is 14.8 cm. Since 1 meter = 100 centimeters, we need to convert the string's length to meters:
[tex]\[
\text{Length in meters} = \frac{14.8 \text{ cm}}{100} = 0.148 \text{ m}
\][/tex]
2. Understand the relationship between the frequency, wave speed, and string length:
The fundamental frequency of a vibrating string is given by:
[tex]\[
f = \frac{v}{2L}
\][/tex]
where:
- [tex]\( f \)[/tex] is the frequency,
- [tex]\( v \)[/tex] is the speed of the wave,
- [tex]\( L \)[/tex] is the length of the string.
3. Insert the given values:
- The speed of the wave (which is typically the speed of sound in air at room temperature) is 334 m/s.
- The length of the string [tex]\( L \)[/tex] is 0.148 meters.
4. Calculate the frequency:
Substituting the given values into the formula:
[tex]\[
f = \frac{334 \text{ m/s}}{2 \times 0.148 \text{ m}}
\][/tex]
Simplifying the denominator:
[tex]\[
2 \times 0.148 \text{ m} = 0.296 \text{ m}
\][/tex]
Now, dividing:
[tex]\[
f = \frac{334}{0.296} \approx 1128.378 \text{ Hz}
\][/tex]
Hence, the frequency of the unmarked fork in tune with a 14.8 cm string is approximately 1128.378 Hz.
