To solve the problem regarding how a change in temperature of the medium affects sound waves, we will analyze the relationships between various properties of sound waves: velocity, frequency, wavelength, amplitude, and loudness.
### Step-by-Step Solution:
1. **Understanding the Relationship between Temperature and Velocity**:
- The velocity of sound in a medium is affected by the temperature of that medium. The formula for the velocity (V) of sound in an ideal gas is given by:
\[
V = \sqrt{\frac{\gamma RT}{M}}
\]
where:
- \( \gamma \) = adiabatic index (atomicity of the gas)
- \( R \) = gas constant
- \( T \) = absolute temperature of the medium
- \( M \) = molecular weight of the gas
2. **Effect of Temperature on Velocity**:
- From the formula, we can see that the velocity \( V \) is directly proportional to the square root of the temperature \( T \). Therefore, if the temperature increases, the velocity of sound also increases.
3. **Using the Wave Equation**:
- The relationship between velocity (V), frequency (f), and wavelength (λ) is given by:
\[
V = f \lambda
\]
- Here, \( V \) is the velocity of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength.
4. **Analyzing Frequency**:
- The frequency of a sound wave is determined by the source of the sound and does not change with temperature. Thus, when the temperature changes, the frequency \( f \) remains constant.
5. **Determining the Effect on Wavelength**:
- Since the velocity \( V \) changes with temperature and the frequency \( f \) remains constant, we can deduce that the wavelength \( \lambda \) must change to maintain the relationship:
\[
V = f \lambda
\]
- Therefore, if \( V \) increases due to an increase in temperature, \( \lambda \) must also increase.
6. **Conclusion on Other Properties**:
- Amplitude and loudness are not directly affected by temperature changes. Amplitude is related to the energy of the wave, and loudness is perceived based on amplitude and frequency. Since frequency does not change, loudness remains constant as well.
7. **Final Answer**:
- The only property of sound waves that changes with a change in temperature of the medium is the wavelength. Therefore, the answer is:
- **Wavelength of sound changes**.
