Is synchronization needed while reading if no contention could occur

Consider code sniper below:

package sync;

public class LockQuestion {
    private String mutable;

    public synchronized void setMutable(String mutable) {
        this.mutable = mutable;
    }

    public String getMutable() {
        return mutable;
    }   
}

At time Time1 thread Thread1 will update ‘mutable’ variable. Synchronization is needed in setter in order to flush memory from local cache to main memory. At time Time2 ( Time2 > Time1, no thread contention) thread Thread2 will read value of mutable.

Question is – do I need to put synchronized before getter? Looks like this won’t cause any issues - memory should be up to date and Thread2’s local cache memory should be invalidated&updated by Thread1, but I’m not sure.